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《Acta Analysis Functionalis Applicata》 2009-01
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Superconvergence of Finite Element Methods for Pricing Options

LIN Qun1, ZHANG Shu-hua2 1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 2. Research Center for Mathematics and Economics, Tianjin University of Finance and Economics, Tianjin 300222, China  
We are concerned with finite element methods for pricing American lookback put options. On the basis of converting the problem into the equivalent variational inequality, the semidiscrete scheme is presented, and the L2- and L∞-error estimates are established, respectively. In addition, to enhance further the approximation solutions, by means of a superapproximation analysis technique and an interpolation postprocessing method, we study global superconvergence estimates in H1-norm for linear finite elements. As by-products, the global superconvergence results can be used to generate a posteriori error estimators.
【Fund】: supported in part by the Special Funds for Major State Basic Research Project (2007CB814906);; the National Natural Science Foundation of China (10471019 10471103 and10771158);; Social Science Foundation of the Ministry of Education of China (numerical methods for convertiblebonds 06JA630047);; Tianjin Natural Science Foundation (07JCYBJC14300);; the State Key Laboratory ofScientific and Engineering Computing and Tianjin University of Finance and Economics
【CateGory Index】: O241.82
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